(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
and(tt, X) → activate(X)
isNePal(__(I, __(P, I))) → tt
activate(X) → X
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
and(tt, z0) → activate(z0)
isNePal(__(z0, __(z1, z0))) → tt
activate(z0) → z0
Tuples:
__'(__(z0, z1), z2) → c(__'(z0, __(z1, z2)), __'(z1, z2))
AND(tt, z0) → c3(ACTIVATE(z0))
S tuples:
__'(__(z0, z1), z2) → c(__'(z0, __(z1, z2)), __'(z1, z2))
AND(tt, z0) → c3(ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:
__, and, isNePal, activate
Defined Pair Symbols:
__', AND
Compound Symbols:
c, c3
(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))
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
__(__(z0, z1), z2) → __(z0, __(z1, z2))
__(z0, nil) → z0
__(nil, z0) → z0
and(tt, z0) → activate(z0)
isNePal(__(z0, __(z1, z0))) → tt
activate(z0) → z0
Tuples:
AND(tt, z0) → c3(ACTIVATE(z0))
S tuples:
AND(tt, z0) → c3(ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:
__, and, isNePal, activate
Defined Pair Symbols:
AND
Compound Symbols:
c3
(5) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing nodes:
AND(tt, z0) → c3(ACTIVATE(z0))
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
__(__(z0, z1), z2) → __(z0, __(z1, z2))
__(z0, nil) → z0
__(nil, z0) → z0
and(tt, z0) → activate(z0)
isNePal(__(z0, __(z1, z0))) → tt
activate(z0) → z0
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
__, and, isNePal, activate
Defined Pair Symbols:none
Compound Symbols:none
(7) SIsEmptyProof (EQUIVALENT transformation)
The set S is empty
(8) BOUNDS(O(1), O(1))