(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(x, x) → f(a, b)
b → c
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, z0) → f(a, b)
b → c
Tuples:
F(z0, z0) → c1(F(a, b), B)
S tuples:
F(z0, z0) → c1(F(a, b), B)
K tuples:none
Defined Rule Symbols:
f, b
Defined Pair Symbols:
F
Compound Symbols:
c1
(3) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing tuple parts
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, z0) → f(a, b)
b → c
Tuples:
F(z0, z0) → c1(F(a, b))
S tuples:
F(z0, z0) → c1(F(a, b))
K tuples:none
Defined Rule Symbols:
f, b
Defined Pair Symbols:
F
Compound Symbols:
c1
(5) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
F(
z0,
z0) →
c1(
F(
a,
b)) by
F(x0, x0) → c1(F(a, c))
F(x0, x0) → c1
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, z0) → f(a, b)
b → c
Tuples:
F(x0, x0) → c1(F(a, c))
F(x0, x0) → c1
S tuples:
F(x0, x0) → c1(F(a, c))
F(x0, x0) → c1
K tuples:none
Defined Rule Symbols:
f, b
Defined Pair Symbols:
F
Compound Symbols:
c1, c1
(7) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing nodes:
F(x0, x0) → c1
F(x0, x0) → c1(F(a, c))
(8) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, z0) → f(a, b)
b → c
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
f, b
Defined Pair Symbols:none
Compound Symbols:none
(9) SIsEmptyProof (EQUIVALENT transformation)
The set S is empty
(10) BOUNDS(O(1), O(1))