(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
U11(tt) → U12(tt)
U12(tt) → tt
isNePal(__(I, __(P, I))) → U11(tt)
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
__(__(z0, z1), z2) → __(z0, __(z1, z2))
__(z0, nil) → z0
__(nil, z0) → z0
U11(tt) → U12(tt)
U12(tt) → tt
isNePal(__(z0, __(z1, z0))) → U11(tt)
Tuples:
__'(__(z0, z1), z2) → c(__'(z0, __(z1, z2)), __'(z1, z2))
U11'(tt) → c3(U12'(tt))
ISNEPAL(__(z0, __(z1, z0))) → c5(U11'(tt))
S tuples:
__'(__(z0, z1), z2) → c(__'(z0, __(z1, z2)), __'(z1, z2))
U11'(tt) → c3(U12'(tt))
ISNEPAL(__(z0, __(z1, z0))) → c5(U11'(tt))
K tuples:none
Defined Rule Symbols:
__, U11, U12, isNePal
Defined Pair Symbols:
__', U11', ISNEPAL
Compound Symbols:
c, c3, c5
(3) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
__'(__(z0, z1), z2) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ISNEPAL(__(z0, __(z1, z0))) → c5(U11'(tt))
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
__(__(z0, z1), z2) → __(z0, __(z1, z2))
__(z0, nil) → z0
__(nil, z0) → z0
U11(tt) → U12(tt)
U12(tt) → tt
isNePal(__(z0, __(z1, z0))) → U11(tt)
Tuples:
U11'(tt) → c3(U12'(tt))
S tuples:
U11'(tt) → c3(U12'(tt))
K tuples:none
Defined Rule Symbols:
__, U11, U12, isNePal
Defined Pair Symbols:
U11'
Compound Symbols:
c3
(5) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing nodes:
U11'(tt) → c3(U12'(tt))
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
__(__(z0, z1), z2) → __(z0, __(z1, z2))
__(z0, nil) → z0
__(nil, z0) → z0
U11(tt) → U12(tt)
U12(tt) → tt
isNePal(__(z0, __(z1, z0))) → U11(tt)
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
__, U11, U12, isNePal
Defined Pair Symbols:none
Compound Symbols:none
(7) SIsEmptyProof (EQUIVALENT transformation)
The set S is empty
(8) BOUNDS(O(1), O(1))