0 QTRS
↳1 AAECC Innermost (⇔)
↳2 QTRS
↳3 DependencyPairsProof (⇔)
↳4 QDP
↳5 DependencyGraphProof (⇔)
↳6 AND
↳7 QDP
↳8 UsableRulesProof (⇔)
↳9 QDP
↳10 QReductionProof (⇔)
↳11 QDP
↳12 QDPSizeChangeProof (⇔)
↳13 TRUE
↳14 QDP
↳15 UsableRulesProof (⇔)
↳16 QDP
↳17 QReductionProof (⇔)
↳18 QDP
↳19 Narrowing (⇔)
↳20 QDP
↳21 Rewriting (⇔)
↳22 QDP
↳23 Rewriting (⇔)
↳24 QDP
↳25 Rewriting (⇔)
↳26 QDP
↳27 Rewriting (⇔)
↳28 QDP
↳29 Narrowing (⇔)
↳30 QDP
↳31 DependencyGraphProof (⇔)
↳32 QDP
↳33 Narrowing (⇔)
↳34 QDP
↳35 Rewriting (⇔)
↳36 QDP
↳37 Rewriting (⇔)
↳38 QDP
↳39 Rewriting (⇔)
↳40 QDP
↳41 Rewriting (⇔)
↳42 QDP
↳43 Narrowing (⇔)
↳44 QDP
↳45 DependencyGraphProof (⇔)
↳46 QDP
↳47 Narrowing (⇔)
↳48 QDP
↳49 DependencyGraphProof (⇔)
↳50 QDP
↳51 Rewriting (⇔)
↳52 QDP
↳53 Narrowing (⇔)
↳54 QDP
↳55 DependencyGraphProof (⇔)
↳56 QDP
↳57 Narrowing (⇔)
↳58 QDP
↳59 DependencyGraphProof (⇔)
↳60 QDP
↳61 Rewriting (⇔)
↳62 QDP
↳63 Narrowing (⇔)
↳64 QDP
↳65 DependencyGraphProof (⇔)
↳66 QDP
↳67 Rewriting (⇔)
↳68 QDP
↳69 UsableRulesProof (⇔)
↳70 QDP
↳71 Rewriting (⇔)
↳72 QDP
↳73 Narrowing (⇔)
↳74 QDP
↳75 DependencyGraphProof (⇔)
↳76 QDP
↳77 Narrowing (⇔)
↳78 QDP
↳79 DependencyGraphProof (⇔)
↳80 QDP
↳81 UsableRulesProof (⇔)
↳82 QDP
↳83 QReductionProof (⇔)
↳84 QDP
↳85 Rewriting (⇔)
↳86 QDP
↳87 UsableRulesProof (⇔)
↳88 QDP
↳89 QReductionProof (⇔)
↳90 QDP
↳91 Rewriting (⇔)
↳92 QDP
↳93 Instantiation (⇔)
↳94 QDP
↳95 DependencyGraphProof (⇔)
↳96 QDP
↳97 Instantiation (⇔)
↳98 QDP
↳99 DependencyGraphProof (⇔)
↳100 QDP
↳101 UsableRulesProof (⇔)
↳102 QDP
↳103 QReductionProof (⇔)
↳104 QDP
↳105 Instantiation (⇔)
↳106 QDP
↳107 DependencyGraphProof (⇔)
↳108 AND
↳109 QDP
↳110 QDPSizeChangeProof (⇔)
↳111 TRUE
↳112 QDP
↳113 QDPSizeChangeProof (⇔)
↳114 TRUE
cond1(true, x, y) → cond2(gr(x, 0), x, y)
cond2(true, x, y) → cond1(or(gr(x, 0), gr(y, 0)), p(x), y)
cond2(false, x, y) → cond3(gr(y, 0), x, y)
cond3(true, x, y) → cond1(or(gr(x, 0), gr(y, 0)), x, p(y))
cond3(false, x, y) → cond1(or(gr(x, 0), gr(y, 0)), x, y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
cond1(true, x, y) → cond2(gr(x, 0), x, y)
cond2(true, x, y) → cond1(or(gr(x, 0), gr(y, 0)), p(x), y)
cond2(false, x, y) → cond3(gr(y, 0), x, y)
cond3(true, x, y) → cond1(or(gr(x, 0), gr(y, 0)), x, p(y))
cond3(false, x, y) → cond1(or(gr(x, 0), gr(y, 0)), x, y)
cond1(true, x, y) → cond2(gr(x, 0), x, y)
cond2(true, x, y) → cond1(or(gr(x, 0), gr(y, 0)), p(x), y)
cond2(false, x, y) → cond3(gr(y, 0), x, y)
cond3(true, x, y) → cond1(or(gr(x, 0), gr(y, 0)), x, p(y))
cond3(false, x, y) → cond1(or(gr(x, 0), gr(y, 0)), x, y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
cond1(true, x0, x1)
cond2(true, x0, x1)
cond2(false, x0, x1)
cond3(true, x0, x1)
cond3(false, x0, x1)
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND1(true, x, y) → COND2(gr(x, 0), x, y)
COND1(true, x, y) → GR(x, 0)
COND2(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), p(x), y)
COND2(true, x, y) → OR(gr(x, 0), gr(y, 0))
COND2(true, x, y) → GR(x, 0)
COND2(true, x, y) → GR(y, 0)
COND2(true, x, y) → P(x)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND2(false, x, y) → GR(y, 0)
COND3(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, p(y))
COND3(true, x, y) → OR(gr(x, 0), gr(y, 0))
COND3(true, x, y) → GR(x, 0)
COND3(true, x, y) → GR(y, 0)
COND3(true, x, y) → P(y)
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND3(false, x, y) → OR(gr(x, 0), gr(y, 0))
COND3(false, x, y) → GR(x, 0)
COND3(false, x, y) → GR(y, 0)
GR(s(x), s(y)) → GR(x, y)
cond1(true, x, y) → cond2(gr(x, 0), x, y)
cond2(true, x, y) → cond1(or(gr(x, 0), gr(y, 0)), p(x), y)
cond2(false, x, y) → cond3(gr(y, 0), x, y)
cond3(true, x, y) → cond1(or(gr(x, 0), gr(y, 0)), x, p(y))
cond3(false, x, y) → cond1(or(gr(x, 0), gr(y, 0)), x, y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
cond1(true, x0, x1)
cond2(true, x0, x1)
cond2(false, x0, x1)
cond3(true, x0, x1)
cond3(false, x0, x1)
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
GR(s(x), s(y)) → GR(x, y)
cond1(true, x, y) → cond2(gr(x, 0), x, y)
cond2(true, x, y) → cond1(or(gr(x, 0), gr(y, 0)), p(x), y)
cond2(false, x, y) → cond3(gr(y, 0), x, y)
cond3(true, x, y) → cond1(or(gr(x, 0), gr(y, 0)), x, p(y))
cond3(false, x, y) → cond1(or(gr(x, 0), gr(y, 0)), x, y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
cond1(true, x0, x1)
cond2(true, x0, x1)
cond2(false, x0, x1)
cond3(true, x0, x1)
cond3(false, x0, x1)
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
GR(s(x), s(y)) → GR(x, y)
cond1(true, x0, x1)
cond2(true, x0, x1)
cond2(false, x0, x1)
cond3(true, x0, x1)
cond3(false, x0, x1)
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
cond1(true, x0, x1)
cond2(true, x0, x1)
cond2(false, x0, x1)
cond3(true, x0, x1)
cond3(false, x0, x1)
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
GR(s(x), s(y)) → GR(x, y)
From the DPs we obtained the following set of size-change graphs:
COND2(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), p(x), y)
COND1(true, x, y) → COND2(gr(x, 0), x, y)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, p(y))
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
cond1(true, x, y) → cond2(gr(x, 0), x, y)
cond2(true, x, y) → cond1(or(gr(x, 0), gr(y, 0)), p(x), y)
cond2(false, x, y) → cond3(gr(y, 0), x, y)
cond3(true, x, y) → cond1(or(gr(x, 0), gr(y, 0)), x, p(y))
cond3(false, x, y) → cond1(or(gr(x, 0), gr(y, 0)), x, y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
cond1(true, x0, x1)
cond2(true, x0, x1)
cond2(false, x0, x1)
cond3(true, x0, x1)
cond3(false, x0, x1)
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), p(x), y)
COND1(true, x, y) → COND2(gr(x, 0), x, y)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, p(y))
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
cond1(true, x0, x1)
cond2(true, x0, x1)
cond2(false, x0, x1)
cond3(true, x0, x1)
cond3(false, x0, x1)
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
cond1(true, x0, x1)
cond2(true, x0, x1)
cond2(false, x0, x1)
cond3(true, x0, x1)
cond3(false, x0, x1)
COND2(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), p(x), y)
COND1(true, x, y) → COND2(gr(x, 0), x, y)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, p(y))
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(true, 0, y1) → COND1(or(false, gr(y1, 0)), p(0), y1)
COND2(true, s(x0), y1) → COND1(or(true, gr(y1, 0)), p(s(x0)), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(or(gr(y0, 0), true), p(y0), s(x0))
COND1(true, x, y) → COND2(gr(x, 0), x, y)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, p(y))
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND2(true, 0, y1) → COND1(or(false, gr(y1, 0)), p(0), y1)
COND2(true, s(x0), y1) → COND1(or(true, gr(y1, 0)), p(s(x0)), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(or(gr(y0, 0), true), p(y0), s(x0))
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, y1)
COND1(true, x, y) → COND2(gr(x, 0), x, y)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, p(y))
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND2(true, s(x0), y1) → COND1(or(true, gr(y1, 0)), p(s(x0)), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(or(gr(y0, 0), true), p(y0), s(x0))
COND2(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, y1)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(true, s(x0), y1) → COND1(true, p(s(x0)), y1)
COND1(true, x, y) → COND2(gr(x, 0), x, y)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, p(y))
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(or(gr(y0, 0), true), p(y0), s(x0))
COND2(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, y1)
COND2(true, s(x0), y1) → COND1(true, p(s(x0)), y1)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND1(true, x, y) → COND2(gr(x, 0), x, y)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, p(y))
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, y1)
COND2(true, s(x0), y1) → COND1(true, p(s(x0)), y1)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND1(true, x, y) → COND2(gr(x, 0), x, y)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, p(y))
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, y1)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, p(y))
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, y1)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(true, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, p(y))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(or(true, gr(y1, 0)), s(x0), p(y1))
COND3(true, y0, 0) → COND1(or(gr(y0, 0), false), y0, p(0))
COND3(true, y0, s(x0)) → COND1(or(gr(y0, 0), true), y0, p(s(x0)))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(or(true, gr(y1, 0)), s(x0), p(y1))
COND3(true, y0, 0) → COND1(or(gr(y0, 0), false), y0, p(0))
COND3(true, y0, s(x0)) → COND1(or(gr(y0, 0), true), y0, p(s(x0)))
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, y0, 0) → COND1(or(gr(y0, 0), false), y0, p(0))
COND3(true, y0, s(x0)) → COND1(or(gr(y0, 0), true), y0, p(s(x0)))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(true, y0, 0) → COND1(or(gr(y0, 0), false), y0, 0)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, y0, s(x0)) → COND1(or(gr(y0, 0), true), y0, p(s(x0)))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, 0) → COND1(or(gr(y0, 0), false), y0, 0)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(true, y0, s(x0)) → COND1(true, y0, p(s(x0)))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, 0) → COND1(or(gr(y0, 0), false), y0, 0)
COND3(true, y0, s(x0)) → COND1(true, y0, p(s(x0)))
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, x, y) → COND3(gr(y, 0), x, y)
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, 0) → COND1(or(gr(y0, 0), false), y0, 0)
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(false, y0, 0) → COND3(false, y0, 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, 0) → COND1(or(gr(y0, 0), false), y0, 0)
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, x, y) → COND1(or(gr(x, 0), gr(y, 0)), x, y)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(false, 0, y1) → COND1(or(false, gr(y1, 0)), 0, y1)
COND3(false, s(x0), y1) → COND1(or(true, gr(y1, 0)), s(x0), y1)
COND3(false, y0, 0) → COND1(or(gr(y0, 0), false), y0, 0)
COND3(false, y0, s(x0)) → COND1(or(gr(y0, 0), true), y0, s(x0))
COND2(false, y0, 0) → COND3(false, y0, 0)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(false, 0, y1) → COND1(or(false, gr(y1, 0)), 0, y1)
COND3(false, s(x0), y1) → COND1(or(true, gr(y1, 0)), s(x0), y1)
COND3(false, y0, 0) → COND1(or(gr(y0, 0), false), y0, 0)
COND3(false, y0, s(x0)) → COND1(or(gr(y0, 0), true), y0, s(x0))
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(false, 0, y1) → COND1(or(false, gr(y1, 0)), 0, y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(or(true, gr(y1, 0)), s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(false, y0, 0) → COND1(or(gr(y0, 0), false), y0, 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND3(false, 0, y1) → COND1(or(false, gr(y1, 0)), 0, y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(false, y0, 0) → COND1(or(gr(y0, 0), false), y0, 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(false, 0, 0) → COND1(or(false, false), 0, 0)
COND3(false, 0, s(x0)) → COND1(or(false, true), 0, s(x0))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(false, y0, 0) → COND1(or(gr(y0, 0), false), y0, 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND3(false, 0, 0) → COND1(or(false, false), 0, 0)
COND3(false, 0, s(x0)) → COND1(or(false, true), 0, s(x0))
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, y0, 0) → COND1(or(gr(y0, 0), false), y0, 0)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(false, 0, 0) → COND1(or(false, false), 0, 0)
COND3(false, s(x0), 0) → COND1(or(true, false), s(x0), 0)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND3(false, 0, 0) → COND1(or(false, false), 0, 0)
COND3(false, s(x0), 0) → COND1(or(true, false), s(x0), 0)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), 0) → COND1(or(true, false), s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, 0) → COND1(or(gr(y0, 0), false), p(y0), 0)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(true, 0, 0) → COND1(or(false, false), p(0), 0)
COND2(true, s(x0), 0) → COND1(or(true, false), p(s(x0)), 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(true, 0, 0) → COND1(or(false, false), p(0), 0)
COND2(true, s(x0), 0) → COND1(or(true, false), p(s(x0)), 0)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(or(true, false), p(s(x0)), 0)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(true, s(x0), 0) → COND1(true, p(s(x0)), 0)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, p(s(x0)), 0)
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, p(s(x0)), 0)
p(s(x)) → x
p(0) → 0
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(x, true) → true
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, y0, s(x0)) → COND1(true, p(y0), s(x0))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
p(s(x)) → x
p(0) → 0
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(x, true) → true
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND2(true, 0, s(y1)) → COND1(true, 0, s(y1))
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND2(true, 0, s(y1)) → COND1(true, 0, s(y1))
p(s(x)) → x
p(0) → 0
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(x, true) → true
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, 0, y1) → COND1(or(false, gr(y1, 0)), 0, p(y1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
p(s(x)) → x
p(0) → 0
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(x, true) → true
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(true, 0, 0) → COND1(or(false, false), 0, p(0))
COND3(true, 0, s(x0)) → COND1(or(false, true), 0, p(s(x0)))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(true, 0, 0) → COND1(or(false, false), 0, p(0))
COND3(true, 0, s(x0)) → COND1(or(false, true), 0, p(s(x0)))
p(s(x)) → x
p(0) → 0
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(x, true) → true
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(true, 0, s(x0)) → COND1(or(false, true), 0, p(s(x0)))
p(s(x)) → x
p(0) → 0
gr(0, x) → false
gr(s(x), 0) → true
or(false, false) → false
or(x, true) → true
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(true, 0, s(x0)) → COND1(or(false, true), 0, p(s(x0)))
or(x, true) → true
p(s(x)) → x
p(0) → 0
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
gr(0, x0)
gr(s(x0), 0)
gr(s(x0), s(x1))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(true, 0, s(x0)) → COND1(or(false, true), 0, p(s(x0)))
or(x, true) → true
p(s(x)) → x
p(0) → 0
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND3(true, 0, s(x0)) → COND1(true, 0, p(s(x0)))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(true, 0, s(x0)) → COND1(true, 0, p(s(x0)))
or(x, true) → true
p(s(x)) → x
p(0) → 0
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(true, 0, s(x0)) → COND1(true, 0, p(s(x0)))
p(s(x)) → x
p(0) → 0
or(false, false)
or(true, x0)
or(x0, true)
p(0)
p(s(x0))
or(false, false)
or(true, x0)
or(x0, true)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(true, 0, s(x0)) → COND1(true, 0, p(s(x0)))
p(s(x)) → x
p(0) → 0
p(0)
p(s(x0))
COND3(true, 0, s(x0)) → COND1(true, 0, x0)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, y0, 0) → COND3(false, y0, 0)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(true, 0, s(x0)) → COND1(true, 0, x0)
p(s(x)) → x
p(0) → 0
p(0)
p(s(x0))
COND2(false, 0, 0) → COND3(false, 0, 0)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND3(false, s(x0), y1) → COND1(true, s(x0), y1)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(false, s(x0), 0) → COND1(true, s(x0), 0)
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(true, 0, s(x0)) → COND1(true, 0, x0)
COND2(false, 0, 0) → COND3(false, 0, 0)
p(s(x)) → x
p(0) → 0
p(0)
p(s(x0))
COND2(false, y0, s(x0)) → COND3(true, y0, s(x0))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(true, 0, s(x0)) → COND1(true, 0, x0)
p(s(x)) → x
p(0) → 0
p(0)
p(s(x0))
COND2(false, 0, s(x1)) → COND3(true, 0, s(x1))
COND3(true, s(x0), y1) → COND1(true, s(x0), p(y1))
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND3(true, 0, s(x0)) → COND1(true, 0, x0)
COND2(false, 0, s(x1)) → COND3(true, 0, s(x1))
p(s(x)) → x
p(0) → 0
p(0)
p(s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, 0, s(x1)) → COND3(true, 0, s(x1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(true, 0, s(x0)) → COND1(true, 0, x0)
p(s(x)) → x
p(0) → 0
p(0)
p(s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, 0, s(x1)) → COND3(true, 0, s(x1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(true, 0, s(x0)) → COND1(true, 0, x0)
p(0)
p(s(x0))
p(0)
p(s(x0))
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, 0, s(x1)) → COND3(true, 0, s(x1))
COND3(true, y0, s(x0)) → COND1(true, y0, x0)
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(true, 0, s(x0)) → COND1(true, 0, x0)
COND3(true, 0, s(z0)) → COND1(true, 0, z0)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND1(true, 0, y1) → COND2(false, 0, y1)
COND2(false, 0, s(x1)) → COND3(true, 0, s(x1))
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
COND3(true, 0, s(x0)) → COND1(true, 0, x0)
COND2(false, 0, s(x1)) → COND3(true, 0, s(x1))
COND3(true, 0, s(x0)) → COND1(true, 0, x0)
COND1(true, 0, y1) → COND2(false, 0, y1)
From the DPs we obtained the following set of size-change graphs:
COND1(true, s(x0), y1) → COND2(true, s(x0), y1)
COND2(true, s(x0), y1) → COND1(true, x0, y1)
COND2(true, s(x0), 0) → COND1(true, x0, 0)
COND2(true, s(x0), s(y1)) → COND1(true, x0, s(y1))
From the DPs we obtained the following set of size-change graphs: